Deriving object visibilities from interferograms obtained with a fiber stellar interferometer

A method is given for extracting object visibilities from data provided by a long baseline interferometer, where the beams are spatially filtered by single-mode fibers and interferograms are obtained as scans around the zero optical pathlength difference. It is shown how the signals can be corrected from the wavefront perturbations caused by atmospheric turbulence. If the piston perturbations are also removed, then the corrected data contain both spatial and spectral information on the source (double Fourier interferometry). When the piston cannot be removed, object phase and spectral information are lost, and the observable (free of detector noise bias) is the squared modulus of the coherence factor, integrated over the optical bandpass. In a fiber interferometer this quantity leads to very accurate object visibility measurements because the transfer function does not involve an atmospheric term. The analysis also holds for a more classical pupil plane interferometer which does not take advantage of the spatial filtering capability of single-mode fibers. In that case however, the transfer function includes a turbulence term that needs to be calibrated by statistical methods.